You got the half life part, but just to expand on it. If you are doing a test that lasts maybe an hour, you don't want to leave radiation around any longer than you need to. So the short half life material will disappear much faster. After 20 half lives it has decreased by a factor of over a million. So if it had a half life of 3 hours, 20 half lives is 60 hours, two and a half days.

You won't want to drink the water with either beta or gamma emitters in it. Your class should have taught you something about protection from these radiation sources. If it didn't, you need to do some reading on beta and gamma radiation protection. Google for it, and take a look on Wikipedia.

Beta particles, at least for common energies from radioactive decay, are stopped by very thin shielding. Most of the time they will be stopped by your clothes or even by the outer dead layer of your skin. So as long as you don't ingest it (eat, drink, breathe) a beta emitter is unlikely to cause harm. If you ingest it then the emitter is going to be mixed into your cells and so can cause harm.

Gamma rays have much more penetrating power. To shield from gamma you want mass, in particular you want lots of protons. Often lead is used because it is very dense and, compared to other materials of similar density, fairly cheap and easy to obtain. But any kind of matter will provide some shielding. You just need thicker shielding for less dense material.

So now think about detecting these particles on the other side of some ground, and through a pipe.

Beta particles, at least for common energies from radioactive decay, are stopped by very thin shielding. Most of the time they will be stopped by your clothes or even by the outer dead layer of your skin.